Theoretical prediction of ground vibrations from underground trains

Generation of ground vibrations by underground trains is investigated theoretically in the low-frequency approximation, i.e. for characteristic wave-lengths of generated bulk acoustic waves in the ground essentially larger than the diameter of the tunnel. The corresponding numerical calculations show that for most of the practical values of a tunnel depth, the main contribution to the vertical component of the surface ground vibration velocity is due to the radiated shear bulk waves rather than to the longitudinal ones. Comparison of the ground vibration spectra generated by typical underground trains with the spectra of the above-ground trains shows that the shapes of these spectra are similar. This implies that one can use for underground trains the same methods of suppressing ground vibrations at speed-dependent frequencies that can be used for above-ground trains, e.g., by choosing special relations between the track and train parameters.